What if the two sides just can't reach a deal? Who stands to lose?
With an Aug. 2 deadline to resolve the issue approaching, the questions are growing less hypothetical by the day. One prominent commentator, conservative New York Times columnist David Brooks, took sides Tuesday in a sharply-worded column that amounted to a tongue-lashing for the whole Republican Party.
"If the debt ceiling talks fail, independent voters will see that Democrats were willing to compromise but Republicans were not," writes Mr. Brooks, who is also a frequent TV commentator on the PBS NewsHour. "If responsible Republicans don't take control, independents will conclude that Republican fanaticism caused this default. They will conclude that Republicans are not fit to govern."
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Brooks stirred up a kind of hornets' nest of discussion by asserting that the Republican Party is so fixated on one issue – tax levels – that it may have become "an odd protest movement" rather than "a normal conservative party."
Some fellow pundits agreed, while critics said Brooks, not the Republican Party, was unreasonable. A blog post by Timothy Carney at the Washington Examiner said the columnist "loves the imaginary tax deal that exists in his own brain."
The debate over "fanaticism" aside, a crunch time is approaching that could test who wins and loses in a fiscal showdown.
Some recent polls suggest that Brooks may be right on one thing: that Republicans would come out on the losing end, politically, if no deal is reached.
* If Congress does not raise the debt limit, 42 percent of American adults say Republicans will be "mainly responsible," according to a June poll conducted by the Pew Research Center and Washington Post. Some 33 percent cited the Obama administration, and the rest answered both, neither, or unsure.
* When asked how federal deficits should be reduced, 59 percent of Americans say they'd prefer a blend of spending cuts and tax hikes, according to an April ABC News/Washington Post poll. That's far more than the 36 percent who argue only for cutting spending (the approach Republican lawmakers are pushing for). Only 3 percent say to solve the budget problem entirely through tax hikes. A Reuters/Ipsos poll found a similar result.
* Some 50 percent of American adults say they prefer Obama's approach to "tough" budget choices, while 42 percent favored that of Republicans, in a CNN/Opinion Research survey concluded at the beginning of May. On that question, Obama widened his lead since January.
This does not mean US voters are about to stamp the Republican Party with the label Brooks mentioned, "unfit to govern."
The situation is fluid and nuanced.
First, many political analysts say a deal will probably be reached for at least a short-term extension of limit on federal borrowing, to avoid the risk that the US Treasury will default on public debt. Such a short-term fix might stop short of giving Obama any tax hikes or Republicans the level of spending cuts they desire.
Second, Americans have plenty of doubts about both parties, showing about the same level of disapproval for Democrats (67 percent) as Republicans (69 percent) when it comes to budget-deficit strategies, according to a June Associated Press/GfK poll.
Specifically, a large majority of the public worries that Democrats won't go far enough to fix runaway deficits, and that they'll be too prone to raise taxes, an April USA Today/Gallup poll found. Conversely, a large majority worries that Republicans will cut Medicare, Social Security, and programs for the poor too deeply, and "protect the rich at the expense of everyone else."
If an impasse over the debt limit persists, financial markets could be roiled by investor anxiety over the risk of a US default. In turn, that could ramp up voter anger against elected officials blamed for failure to reach a compromise.
From that perspective, many policy analysts say that walking away from the bargaining table without a deal would be a bad idea for either party.